The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.

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For better reading, x1 = x, x2 = y, x3 = z

(2) - (1) ====> x - 2y = -5 ===> x = -5 + 2y

(1) + (2) + (3) ====> 6x + 7y = 8

Plug x = -5 + 2y

6 (-5 + 2y) + 7y = 8

-30 + 12y + 7y = 8

19 y = 38

y = 2

x = -5 + 2(2) = -5 + 4 = -1

From (2)

2x - z =-2

2 (-1) - z = -2

z = 0

Therefore x1 = -1, z2 = 2, x3 = 0

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